Interpreting Mean Reversion Implied by Bermudan Swaption Calibration

Summary

The document explains how a calibrated interest-rate model can produce a market-implied mean-reversion parameter. Bermudan swaptions are valued within models that include mean reversion, and calibration selects parameters to fit observed swaption prices. The fitted mean-reversion rate is therefore implied by prices under the chosen model and calibration setup, rather than observed directly.

The answer notes that the parameter may move with other measures of mean reversion, such as estimates from time-series analysis, while its numerical level is only qualitatively informative outside the model framework. The document gives no calibration example, pricing comparison, or empirical results. Interpretation depends on the selected model, its assumptions, calibration instruments, and the fit criterion, so the parameter should not be treated as a model-independent estimate of an underlying economic rate.

Key ideas

• Interest-rate models used to value Bermudan swaptions can include a mean-reversion parameter.
• Calibration to observed swaption prices yields a model-implied, risk-neutral mean-reversion estimate.
• The fitted parameter depends on the model framework and calibration choices.
• The parameter may track other mean-reversion measures, but its level is mainly qualitative outside the calibrated model.

Tags

# How is mean reversion implied by different valuations of Bermudan swaptions?


# How is mean reversion implied by different valuations of Bermudan swaptions?












Someone told me that mean reversion can be implied by the different valuations of bermudan swaptions when using different methods for volatility calibration. Does anyone know what this means?

## Answer by Brian B (score 2)

https://quant.stackexchange.com/a/1668

Bermudan swaptions (often on interest rates) are typically valued with a model that incorporates mean-reversion parameters. This might be as naive as Black-Karasinski, but more often is somewhat more sophisticated, for example Generalized Vasicek.

Calibrating the model involves choosing model parameters that "best" fit the observed bermudan swaption prices. Since one of those parameters is a mean reversion term ($\mu$), after your fitting process you end up with a market-implied risk-neutral estimate of mean reversion rate $\mu$ within that model.

You will find that $\mu$'s magnitude will correlate highly with other measures of mean reversion (say from time series analysis), but that outside your original model framework $\mu$'s actual level is only qualitatively valuable .

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.